Inverter for a distributed power generator

ABSTRACT

Provided is a maximum power point (MPP) tracker for a PV cell inverter, and a PV cell inverter. The MPP tracker decouples output power oscillations from the input power generation and extracts maximum available power from the PV cell. The PV cell inverter uses the MPP tracker and generates a sinusoidal output current from the MPP tracker output. The sinusoidal output current may be fed to a power distribution grid. The PV cell inverter may use a pulse width modulation technique to cancel harmonics in the sinusoidal output current. The circuits use a minimum number of components and avoid use of large electrolytic capacitors.

RELATED APPLICATIONS

This application is a division of U.S. patent application Ser. No.12/709,166, filed on Feb. 19, 2010, and claims the benefit of the filingdate of U.S. Provisional Patent Application No. 61/202,355, filed onFeb. 20, 2009, the contents of which are incorporated herein byreference in their entirety.

FIELD OF THE INVENTION

This invention relates to circuits, systems, and methods for obtainingpower from a distributed power generator such as a photovoltaic cell,and for interfacing a distributed power generator to a powerdistribution grid. In particular, this invention relates to a maximumpower point tracker and a string/multi-string photovoltaic cell inverterincorporating the maximum power point tracker.

BACKGROUND OF THE INVENTION

Grid-connected distributed power generators such as photovoltaic (PV)systems typically consist of two major parts: PV cell arrays to convertirradiation to electrical energy, and an inverter to feed the electricalenergy into a power distribution grid. PV cell configurations may becategorized according to four groups [1]: centralized, string,multi-string, and AC-module and AC-cell technologies, see FIG. 1(a). Allapproaches have advantages and disadvantages [1], [2], and compromisevarious attributes such as harmonic rejection capability, simplicity,efficiency, flexibility, reliability, safety, modularity, and cost.

The centralized topology is considered the best for high powerapplications because the input power level can be increased, and it usesonly one inverter which increases the conversion efficiency. However,this topology has limitations. For example, since there is significanthigh voltage DC wiring between the PV cells and the inverter, thetopology requires expensive DC switches and special isolation, safety,and protection circuits. Due to the centralized maximum power pointtracking (MPPT), partial shading of the PV cells or any mismatch betweenthe PV cells causes a significant drop in the output power generation.

For medium power applications, the most suitable configuration isconsidered to be the string or multi-string technologies, [3], where oneor more strings of PV cells are connected to a single inverter, as shownin FIG. 1(b). Unlike the centralized configuration, this type ofconfiguration enables independent MPPT for all strings which might beinstalled in different sizes and orientations. This also increases theoverall efficiency under certain circumstances, such as partialshadowing of the PV cells. Therefore, this topology offers theflexibility to optimize the number of strings and inverters for thespecific application power level to increase the overall efficiency andto reduce losses.

Since the PV cell array current-voltage characteristic is highlynonlinear, the MPPT of PV cell arrays is challenging. MPPT systemsusually consist of two parts; MPP tracker hardware, and an algorithm.The MPP tracker alters the input resistance of the inverter seen fromthe output terminal of the PV cells that results in a change of theoperating point. MPPT algorithms [4] calculate the best operating pointavailable based on the current irradiation and temperature of the PVcells and provide a reference point for the MPP tracker hardware.

In single-phase or unbalanced three phase grid-connected systems, theinstantaneous power injected to the grid oscillates at twice the gridfrequency. One of the MPP tracker tasks is to decouple the poweroscillation from the PV cells, because the oscillation results in adeviation from the optimum operating point of the PV cells [2], [5].This problem is usually resolved by connecting a large electrolyticcapacitor at the PV cell terminals, which in turn decreases the lifetimeand increases the volume, weight, and cost of the inverter. To avoid theelectrolytic capacitor, an auxiliary circuit may be used [6], [7] whichdraws constant current from the input and generates a high DC voltage atthe middle stage to supply the pulsation required at the output. In [8],an auxiliary circuit was proposed with a transformer and passive andactive components to avoid oscillation. However, such solutions have lowefficiency and have complex hardware and control systems, which make theoverall system expensive.

SUMMARY OF THE INVENTION

Described herein is a maximum power point (MPP) tracker topology whichdecouples output power oscillations from the PV cell power generation.The topology may extract the maximum available power from each PV cellstring of a multi-string system independently. The circuit uses aminimum number of components and avoids the use of large electrolyticcapacitors, which is a major factor in limiting circuit life time. TheMPP tracker is not limited to low-power applications. Such decoupling,described herein, is applicable to voltage source converter topologiesand current source converter topologies.

One embodiment provides a maximum power point (MPP) tracker for aphotovoltaic cell, comprising: high side and low side input points forthe photovoltaic cell; a capacitor connected across the high side andlow side input points; a switch connected between the high side inputpoint and a node; an inductor connected between the node and a high sideoutput point; a unidirectional conducting device connected between thenode and the low side; a low side output point; and a maximum powerpoint (MPP) tracker controller; wherein the switch controls the voltageacross the capacitor. The capacitor voltage may be controlled between alower limit and an upper limit.

Another embodiment provides a maximum power point (MPP) tracker for aphotovoltaic cell, comprising: high side and low side input points forthe photovoltaic cell; a series input inductor connected to the highside input point; a switch connected between the series input inductorand a node; an output inductor connected between the node and a highside output point; a unidirectional conducting device connected betweenthe node and the low side; a low side output point; and a maximum powerpoint (MPP) tracker controller; wherein the switch controls the currentthrough the inductor. The inductor current may be controlled between alower limit and an upper limit.

Also described herein is a PV cell inverter using a current source(e.g., buck-boost) topology in which the output voltage may be greateror smaller than the voltage of the input PV cell. Unlike voltage sourcetopologies, the inverter directly generates and feeds the desiredcurrent into the grid using a modified pulse width modulation (PWM)technique. The modified PWM technique and control strategy optimize themiddle stage dc current level in the inverter. This results in a flatterefficiency curve for a wide range of input power. The PV cell maycomprise a string of multiple PV cells, or multiple strings of PV cells.

Also described herein is an inverter for a photovoltaic cell,comprising: an MPP tracker as described above; and a means forgenerating a sinusoidal output current from the MPP tracker output.

The means for generating a sinusoidal output current may comprise acurrent source inverter or a voltage source inverter. In one embodiment,the means for generating a sinusoidal. output current may comprise apulse width modulator. The means for generating a sinusoidal outputcurrent may comprise a means that modifies a pulse width modulationreference signal to cancel harmonics in an output current of theinverter. The means that modifies a pulse width modulation referencesignal may comprise a PI controller and a compensator.

Also described herein is a method of applying a maximum power pointtracker to a photovoltaic cell, comprising: connecting the outputvoltage of the photovoltaic cell across a capacitor; maintaining voltageacross the capacitor between a lower limit and an upper limit to produceoutput power; wherein the upper limit is a reference voltage; whereinthe lower limit is a function of a selected switching frequency of aswitching circuit and an output current of the photovoltaic cell;wherein the output power is the maximum power available from thephotovoltaic cell at a given instant in time.

The method may comprise connecting the output voltage of a string of twoor more photovoltaic cells across the capacitor. The method may compriseusing a switching circuit to maintain the voltage across the capacitor.

Another aspect relates to a method for obtaining power from aphotovoltaic cell, comprising: using the maximum power point trackerwith the photovoltaic cell and producing output power according to themethod described above; and generating a sinusoidal output current fromthe output power.

The method may comprise using pulse width modulation (PWM) to generatethe sinusoidal output voltage or current. The method may comprise usingpulse width modulation to cancel a harmonic in the output voltage orcurrent. Generating a sinusoidal output current may comprise using acurrent source inverter or a voltage source inverter. The method maycomprise connecting the sinusoidal output current to a powerdistribution grid. The method may comprise connecting the output voltageof a string of two or more photovoltaic cells across the capacitor.

Another aspect relates to a method for obtaining power from a pluralityof photovoltaic cells, comprising: tracking the maximum power point ofeach photovoltaic cell and producing output power from each photovoltaiccell using the method described above; and generating a sinusoidaloutput current from the output power.

Also described herein is a method for obtaining power from a pluralityof photovoltaic cells, comprising: using a maximum power point trackerwith each string of photovoltaic cells or modules and producing outputpower from each string of photovoltaic cells or modules according to themethod of described above; and generating a sinusoidal output currentfrom the output power.

Also described herein is a method of cancelling a harmonic in an outputvoltage or current of a circuit, comprising using a PWM technique. Usinga PWM technique may comprise using a modified PWM technique. Themodified PWM technique may comprise modifying a PWM reference signal toincrease or decrease output current and power of the circuit. Theharmonic may be related to an oscillation of an input voltage or currentof the circuit. The circuit may be a current source inverter or avoltage source inverter.

Also described herein is a PV cell system for connecting PV cells to apower distribution grid, comprising a PV cell inverter as describedherein and one or more PV cells.

The topologies described herein accept low PV cell voltages at theinput, which increases efficiency in partial shading conditions,compared to topologies in which many PV cells are connected in series tobuild up a high input voltage.

Also described herein is a circuit for use with a distributed powergenerator, comprising: a high side input point and a low side inputpoint for the distributed power generator; a high side output point anda low side output point; and (i) a parallel input capacitor; and a meansthat regulates voltage across the capacitor; wherein regulating voltageacross the capacitor substantially removes distributed power generatorinput voltage oscillation; or (ii) a series input inductor; and a meansthat regulates current through the series input inductor; whereinregulating current through the series input inductor substantiallyremoves distributed power generator input current oscillation.

The voltage across the capacitor may be regulated between a lower limitand an upper limit. The means that regulates voltage across thecapacitor may comprise a switch connected between the high side inputpoint and a node; an output inductor connected between the node and thehigh side output point; and a diode connected between the node and thelow side output point. The upper limit may be a reference voltage andthe lower limit may be calculated so that a switching frequency of theswitch and the distributed power generator input voltage oscillation orinput current oscillation do not exceed selected values. The referencevoltage may be obtained from a maximum power point tracking (MPPT)algorithm. The circuit may include a controller for the switch. Thecontroller may be a hysteresis controller.

The current through the series input inductor may be regulated between alower limit and an upper limit. The means that regulates current throughthe series input inductor may comprise: a switch connected between theseries input inductor output and the low side input point; and a diodeconnected in series between the series input inductor and the high sideoutput point. The upper limit may be a reference current and the lowerlimit may be calculated so that a switching frequency of the switch andthe distributed power generator input current oscillation do not exceedselected values. The reference current may be obtained from a maximumpower point tracking (MPPT) algorithm. The circuit may include acontroller for the switch. The controller may be a hysteresiscontroller.

Also described herein is an inverter for a distributed power generator,comprising: the circuit described above; and a means that generates asinusoidal output current from the circuit output. In one embodiment ofthe inverter, (i) the circuit includes a parallel input capacitor and ameans that regulates voltage across the capacitor, and the invertercomprises a current source inverter; or (ii) the circuit includes aseries input inductor and a means that regulates current through theseries input inductor, and the inverter comprises a voltage sourceinverter.

Also described herein is a compensator for use with a voltage sourceinverter or a current source inverter, wherein the compensator modifiesa pulse width modulation (PWM) reference signal of the voltage sourceinverter or current source inverter, to cancel one or more harmonic inthe voltage source inverter or current source inverter output current.

Also described herein is an inverter as described above, including acompensator, wherein the compensator modifies a pulse width modulation(PWM) reference signal of the voltage source inverter or the currentsource inverter, to cancel one or more harmonic in the voltage sourceinverter or current source inverter output current.

Also described herein is a method for obtaining power from a distributedpower generator, comprising: (i) connecting a capacitor across theoutput voltage of the distributed power generator; and activelyregulating voltage across the capacitor; wherein regulating voltageacross the capacitor substantially removes distributed power generatorvoltage oscillation; or (ii) connecting a series input inductor to theoutput of the distributed power generator; and actively regulatingcurrent through the inductor; wherein regulating current through theinductor substantially removes distributed power generator currentoscillation.

The method may comprise: (i) using a switch to regulate the voltageacross the capacitor; or (ii) using a switch to regulate the currentthrough the inductor. The method may include regulating the voltageacross the capacitor between an upper limit and a lower limit. The upperlimit may be a reference voltage and the lower limit may be calculatedso that a switching frequency of the switch and the distributed powergenerator input voltage oscillation or input current oscillation do notexceed selected values. The method may include using hysteresis tocontrol the switch.

Also described herein is a method for obtaining power from a distributedpower generator and producing a sinusoidal output current, comprising:(i) connecting a capacitor across the output voltage of the distributedpower generator; actively regulating voltage across the capacitor tosubstantially remove distributed power generator voltage oscillation;and using a current source inverter to produce the sinusoidal outputcurrent; or (ii) connecting a series input inductor to the output of thedistributed power generator; actively regulating current through theinductor to substantially remove distributed power generator currentoscillation; and using a voltage source inverter to produce thesinusoidal output current.

The method may further comprise connecting the sinusoidal output voltageor current to a power distribution grid.

Also described herein is a method of obtaining power from voltage sourceinverter or a current source inverter, comprising modifying a pulsewidth modulation (PWM) reference signal of the voltage source inverteror current source inverter to cancel one or more harmonic in the voltagesource inverter or current source inverter output current. The methodmay further comprising modifying a pulse width modulation (PWM)reference signal of the voltage source inverter or current sourceinverter to cancel one or more harmonic in the voltage source inverteror current source inverter output current.

In the above embodiments, the distributed power generator may be a windturbine or a photovoltaic cell.

BRIEF DESCRIPTION OF THE DRAWINGS

For a better understanding of the invention, and to show more clearlyhow it may be carried into effect, embodiments will now be described, byway of example, with reference to the accompanying drawings, wherein:

FIG. 1A shows a block diagram of PV cell systems categorized bydifferent PV cell configurations and inverter types, according to theprior art.

FIG. 1B shows a block diagram of a multi-string PV cell inverterconfiguration, according to the prior art.

FIG. 2 is a generalized block diagram of a PV cell inverter according toan aspect of the invention.

FIG. 3A is a schematic diagram of a maximum power point tracker circuitand a controller according to one embodiment. The inset plot of V_(pv)as a function of time shows operation of the main switch S_(B) accordingto one embodiment.

FIG. 3B is a schematic diagram of a maximum power point tracker circuitand a controller according to another embodiment. The inset plot ofI_(pv) as a function of time shows operation of the main switch S_(B)according to the embodiment.

FIG. 3C shows only the ripple of the PV cell voltage, power, and currentwaveforms during three switching cycles of the embodiment of FIG. 3A.

FIGS. 4A and 4B show voltage and current waveforms for the inductorL_(B) in the embodiment of FIG. 3A.

FIG. 5A is a schematic diagram of a single-string grid-connected PV cellinverter according to one embodiment.

FIG. 5B is a schematic diagram of a multi-string grid-connected PV cellinverter based on the single-string embodiment of FIG. 5A.

FIG. 6 shows an embodiment of a modified pulse width modulationtechnique used in the controller for the current source inverter of theembodiment shown in FIG. 5A or 5B.

FIG. 7 is a block diagram of a control scheme for a single-stringinverter according to one embodiment, showing control of the modifiedpulse width modulation technique of FIG. 6.

FIG. 8 is a block diagram of a control scheme for a multi-stringinverter based on the embodiment of FIG. 7.

FIG. 9 is a plot showing output grid current with no harmoniccancellation and a 120 Hz harmonic, then harmonic cancellation, andfinally with a low inductor current reference.

FIG. 10 is a plot showing results of a simulation of the embodimentsshown in FIGS. 5B and 8, under various conditions of irradiance level,input voltage, and partial shading of the PV cells.

DETAILED DESCRIPTION OF EMBODIMENTS

Described herein are systems, circuits, and methods for obtaining powerfrom a distributed power generator, the obtained power being suitablefor injection into a power distribution grid. A distributed powergenerator may be, for example, a wind turbine or a photovoltaic cell.Whereas embodiments of the systems, circuits, and methods are describedherein primarily with respect to photovoltaic cells, it will beappreciated that the systems, circuits, and methods are not limitedthereto.

For example, described herein is an inverter for obtaining power fromone or more photovoltaic cells. In one embodiment, the inverter is forinterfacing one or more PV cells to a power distribution grid. Such anembodiment is shown in FIG. 2. This embodiment includes an inputcapacitor C₁ connected across the PV cell(s) 10, a first stage includingan MPP tracker circuit 20 connected across the input capacitor, and aseries inductor L_(B) connected to the MPP tracker output, and a secondstage including an output inverter, and an output capacitor C_(AC). Thefirst stage also includes a controller 50 for the MPP tracker circuit20, and a circuit 40 to generate a reference voltage. With thecontroller 20, the MPP tracker circuit 20 controls the voltage acrossthe input capacitor C₁. The second stage also includes a controller 60for the inverter 30.

Features of the PV inverter embodiments described herein include: a lowPV cell voltage is accepted, which improves efficiency at partialshading conditions of the PV cells; a wide range of input voltage isaccepted; adaptive control of the inductor L_(B) current DC leveloptimizes the modulation index for the inverter over a wide range ofinput power levels; input and output power decoupling are provided withonly a small input capacitor C₁; a fast MPP tracker; and integration ofthe MPP tracker into a PV cell array is possible because no passivecomponent is required for the input of the MPP tracker stage. Thesefeatures will be described in detail below.

As used herein, the terms “maximum power point tracking (MPPT)” and“maximum power point tracker (MPP tracker)” are distinct. “MPPT” refersto an algorithm and “MPP tracker” refers to hardware (i.e., a circuit).The MPPT calculates the optimum operating point for a distributed powergenerator such as a photovoltaic cell, and provides a reference pointfor MPP tracker to steer the system toward the optimum operating point.

As used herein, the term “photovoltaic cell” refers to any cell having alight absorbing material to absorb photons and generate electrons via aphotoelectric effect. A non-limiting example of a photovoltaic cell is asolar cell. The light absorbing material may absorb light in anywavelength or combination of wavelengths, including, for example,wavelengths of solar light that reach the earth's surface, and/orwavelengths of solar light beyond the earth's atmosphere. Two or morelight absorbing materials having specific wavelengths of lightabsorption may be used in combination to take advantage of differentlight absorption and charge separation mechanisms. The light absorbingmaterial may be configured as, for example, bulk material, thin-film(e.g., inorganic layers, organic dyes, and organic polymers), and/ornanocrystals. The photovoltaic cells may be combined into arrays,strings, or panels.

As used herein, the term “photovoltaic cell string” refers to aplurality of photovoltaic cells connected together in a series,parallel, series-parallel, or other configuration.

Power Decoupling

The instantaneous output power oscillates at twice the grid frequency insingle-phase grid-connected systems. In PV systems, the input powergeneration is dc and thus the oscillation of the instantaneous outputpower, if reflected in the input, causes the input operating point todeviate from dc. If there is power oscillation on the PV side, maximumpower is only achievable at the peak of oscillation, which translatesinto less average power extraction than the available maximum power.This is a power loss that reduces the efficiency of the PV system.Substantially the same problem exists in systems with wind turbines orfuel cells at the input for single phase systems or unbalanced threephase systems. Therefore, power oscillation is a key problem in suchsystems and the converter should decouple the output power oscillationfrom the input dc power generation to maximize efficiency. Powerdecoupling is conventionally performed by using large electrolyticcapacitors in the design to minimize the effect of the output poweroscillation on the input operating point. However, use of largecapacitors lowers the reliability of the hardware, resulting in highmaintenance expenses.

Conventional approaches use a control system to regulate the average ofthe input voltage or current to achieve maximum power point tracking andto reach sufficient amplification gain. In such approaches decoupling isaccomplished by either passive elements or auxiliary power circuits.

In contrast, the maximum power point tracker described herein forces theinput voltage or current to track a reference signal very tightly. As aresult, the double frequency oscillation is displaced and the inputpower generation is at or very close to the optimum dc level.

Power decoupling as described herein may be implemented using a closedloop control system with high bandwidth, such as, for example, ahysteresis controller, or an open loop control system having high gainat the frequency of the oscillatory harmonic. That is, although theoperating point of the converter oscillates at twice the grid frequency,the converter should respond with sufficient speed to reject the effectof this distortion from the power generation (e.g., PV) side.

The high open loop gain or closed loop bandwidth of the system willeventually cause very low or zero steady state error with fast trackingof the input reference point. As a result, input power decoupling isaccomplished only by means of the control strategy and/or the highswitching frequency, rather than methods that use bulky passive elementsor auxiliary circuits. For example, a high switching frequency converterat the PV side as described herein can remove the oscillatory harmonicsat the input. Power decoupling may also be accomplished using a resonantcontroller tuned at the oscillatory harmonic to generate high open loopgain at the PV side converter.

MPP Tracker

FIG. 3A is a schematic diagram of an MPP tracker circuit 20, and itscontroller 50 and reference voltage circuit 40, according to oneembodiment. The inset plot of V_(pv) as a function of time shows anembodiment of a control strategy for this circuit. Other controlstrategies may also be used. In the embodiment shown in FIG. 3A, the MPPtracker circuit includes a series switch S_(B) connected to the highside input terminal and a unidirectional conducting device such as adiode D_(B) connected between the switch output and the low side inputterminal. In operation, the main switch S_(B) is used to regulate theinput capacitor C₁ voltage. Regulating the input voltage enables theinverter to displace output power oscillation from the input terminal,substantially removing PV cell voltage oscillation and avoiding the needfor large input capacitors at the PV terminals. Removal of the inputvoltage oscillation stabilizes the input operating point, resulting inhigh efficiency conversion with much smaller capacitors.

FIG. 3B is a schematic diagram of an MPP tracker circuit 20, and itscontroller 50 and reference voltage circuit 40, according to anotherembodiment. The inset plot of I_(pv) as a function of time shows anembodiment of a control strategy for this circuit. Other controlstrategies may also be used. In the embodiment shown in FIG. 3B, the MPPtracker circuit includes a series input inductor L_(pv), a switch S_(B),and a unidirectional conducting device such as a diode D connected inseries with the high side output terminal. In operation, the main switchS_(B) is used to regulate the current through the inductor L_(pv).Regulating the inductor current enables the inverter to displace outputpower oscillation from the input terminal, substantially removing PVcell voltage oscillation and avoiding the need for large inputcapacitors at the PV terminals. Removal of the input current oscillationstabilizes the input operating point, resulting in high efficiencyconversion with much smaller capacitors.

FIG. 3C shows the ripple of the input voltage, power, and currentwaveforms from the PV cells, for the embodiment of FIG. 3A. A typical PVcell i-v characteristic curve includes three operating conditions: 1)operation at a voltage lower than the optimum point where the PV cellvoltage is increased and the power is increased; 2) operation at avoltage higher than the optimum point where the PV cell voltage isincreased and the power is decreased; and 3) operation around theoptimum point where the PV voltage is increased and the power ismaximum, where the MPP is tracked. It is clear from FIG. 3B that the MPPis tracked since during the rise time of the PV cell voltage, the outputpower reaches its maximum. The control strategy of the above MPP trackerembodiment may accept a reference voltage from any MPP trackingalgorithm (such as, for example, a perturb/observe algorithm), to obtainthe maximum power available from the PV cells independent of the outputvoltage and current. The power is delivered to the inverter stage 30and, as described below, the output current and voltage of the MPPtracker are controlled and induced by the inverter stage. This topologymay provide power to any load or inverter configuration (e.g., voltagesource inverter, current source inverter) at the next stage.

As shown in FIG. 4A, the output of the switch S_(B) is a high frequencyoscillating voltage V_(D). However, the input of the inverter 30 is alow frequency (e.g., twice the grid frequency, 120 Hz) oscillatingvoltage V_(inv). The current in the inductor L_(B) includes dc, anoscillating current at twice the grid frequency, and high frequencyharmonics. Therefore, as shown in FIG. 4B, the inductor current includesa double grid frequency harmonic that should not be injected to theoutput grid current. in one embodiment, described below, the double gridfrequency harmonic is removed using a modified pulse width modulation(PWM) strategy.

Control Strategy for MPP Tracker

An embodiment of the input capacitor C₁ voltage control may be brieflydescribed as follows. The capacitor voltage V_(pv) is maintained betweentwo upper and lower levels. This is done by the hysteresis controlstrategy as shown in FIG. 3A. The controller may be implemented with twocomparators and two comparison levels. The upper level, V_(pv) ^(ref),may be obtained from an MPPT algorithm. The lower level, V_(pv)^(ref)−ΔV_(pv), is not constant and is calculated in such a way that forall conditions, the switching frequency and the voltage ripple do notexceed selected values. This will be shown below. When the inputcapacitor voltage V_(pv) exceeds the upper level, the output of theupper comparator becomes high, the flip-flop is set, which turns themain switch S_(B) on, and discharges the capacitor. The switch remainson until the flip-flop is reset when the capacitor voltage hits thelower limit.

In summary, the controller maintains the PV cell voltage very close tothe optimum reference point provided by the MPPT algorithm. Since thelevel of the input voltage is proportional to the power generation, bycontrolling the input voltage the power fed to the circuit is controlledand this stage becomes a controllable power source. For example, if theoutput of this stage was connected to a heater (e.g., a resistor), theheat transfer would be linearly controlled by the input referencevoltage.

The capacitor value and ΔV_(pv) may be selected such that the operatingfrequency of the circuit is always less than a certain limit and thevoltage ripple is less than %8.5V_(pv) ^(MPP) in order to reach autilization ratio higher than %98. Any ripple at the PV cell voltagedecreases the efficiency (or utilization ratio), because the maximumpower is extracted when the voltage is equal to V_(pv) ^(MPP), and anydeviation due to the voltage ripple decreases the output power.

During the time that the switch S_(B) is off the following relationshipis valid:

$\begin{matrix}{{{\Delta\; Q} = {{C\;\Delta\; V_{pv}} = {\left. {i_{pv}t_{off}}\Rightarrow{\Delta\; V_{pv}} \right. = \frac{i_{pv}}{C_{1}f}}}},{f = \frac{1}{t_{off}}}} & (1)\end{matrix}$

To limit the switching frequency, f is restricted because

$f_{S = \frac{1}{t_{off} + t_{on}}} < {f.}$The equation above shows that

$f = {\frac{i_{pv}}{C_{1}\Delta\; V_{pv}}.}$By substitution it can be shown that if ΔV_(pv) is chosen as

$\frac{i_{pv}}{C_{1}f^{m}},$for all conditions the time off will be almost constant because

${\frac{1}{t_{off}} = {f = f^{m}}},$where f^(m) is the maximum frequency.

The voltage of the PV cells is minimized, i.e., V_(min) ^(MPP), at thelowest operating temperature. As mentioned above, it is desired thatΔV_(pv)<%8.5V_(pv) ^(MPP). Therefore, this inequality holds true for allconditions if ΔV_(pv)<%8.5V_(min) ^(MPP).

From (1) and the above inequality it can be shown that

$\frac{i_{pv}}{C_{1}f^{d}} < {\%\mspace{14mu} 8.5\mspace{14mu}{V_{\min}^{M\; P\; P}.}}$For this inequality to be true for all conditions, the left hand side ismaximized to calculate the capacitor value. The maximum value of the PVcells i_(max) ^(MPP) is known and occurs at irradiation. As a result,the input capacitor C₁ value may be determined as:

$C_{1} = \frac{i_{\max}^{M\; P\; P}}{\%\mspace{14mu} 8.5\mspace{14mu} V_{\min}^{M\; P\; P}f^{m}}$

It is clear from the above equation for C₁ that in obtaining a desiredPV voltage variation, there is a trade-off between the switchingfrequency and the capacitor value. If the parameters are chosen in thisway, this control scheme provides that for all irradiation andtemperature levels the circuit operates below the selected desiredfrequency and the above %98 utilization ratio. For example, if i_(pv)^(max)=4 A, V_(min) ^(MPP)=100 V, and f^(m)=20 KHz, the capacitor willbe C₁=20 μF, where the PV cell voltage variation is selected to beΔV_(pv)=5V.

Current Source PV Cell Inverter

FIG. 5A is a circuit diagram of a single-string PV cell inverteraccording to one embodiment. Shown is the PV cell string 10, the MPPtracker 20, a current source inverter 30, and a low pass filter 70including Cf and Lf to eliminate output current high frequencycomponents. The low pass filter 70 may be replaced by higher orderfilters for a further reduction in the size of the passive components.

FIG. 5B shows a circuit diagram of a multi-string PV cell inverteraccording to another embodiment. This embodiment is based on the circuitof FIG. 5A, but includes two MPP tracker power circuits, and two stringsof PV cell modules. However, any number of power circuits and PV cellstrings may be used. In the first stage the MPP trackers are connectedin parallel, and each MPP tracker is connected to a PV cell string. Thesecond stage includes a current source inverter, which is connected tothe distribution grid. With this embodiment of the control algorithm avoltage source inverter may be used instead of the current sourceinverter, if a small capacitor is used at the input of the voltagesource inverter.

In one embodiment, the controller for the current source inverter uses aPWM scheme. To understand the principle of operation, first assume thatthe current source inverter is fed by a dc current source and the PWMscheme modulates a sinusoidal reference waveform to generate asinusoidal output current, as shown in FIG. 6. As a result of the PWMstrategy the voltage induced at the input of the current source inverteris the modulated grid voltage, full-wave rectified, V_(inv), as shown inFIG. 4A. However, the input of the current source inverter stage isconnected to the MPP tracker output, which is not a constant currentsource. Thus, the input current of the current source inverter changesaccording to the induced voltage as discussed above. Oscillation inducedin the inductor current is inevitable because the input power generationis kept constant by the MPP tracker circuit, but the output poweroscillates at twice the grid frequency and thus, the power oscillationhas to be supplied from an energy storage component, such as theinductors of the MPP tracker circuits. Therefore, the PWM technique maybe modified to generate a pure sinusoidal waveform based on theoscillatory input current source. In one embodiment, shown in FIG. 6,this is accomplished by formulating the inductor current, and thenmodifying the reference signal to the PWM modulator so that it regulatesand controls the dc component of the inductor current i_(L), andprevents the double frequency harmonic component of i_(L) from appearingin the output ac current.

Inductor DC Current Regulation

Inductor current regulation will now be described with respect to PVstring #1 of FIG. 5B. Assume that the converter is lossless(P_(in)=P_(avgo)) and the output filter energy storage is negligible.Also, assume that there is only one PV cell string (string #1) connectedto the circuit. Therefore, the only energy storage component is L_(A).As discussed above, the MPP tracker circuit extracts constant power fromthe PV cells. Assuming that the current source inverter generates acurrent in-phase with the grid voltage, the output power may be derivedas follows:

$\begin{matrix}{{{i_{o}(t)} = {I_{o}\sin\left( {\omega\; t} \right)}},{{v_{o}(t)} = {\left. {V_{o}\sin\left( {\omega\; t} \right)}\Rightarrow{p_{o}(t)} \right. = {\left. {\frac{1}{2}V_{o}I_{o}\left( {1 - {\cos\left( {2\;\omega\; t} \right)}} \right)}\Rightarrow\mspace{250mu} P_{in} \right. = {P_{o}^{avg} = {{\frac{1}{2\pi}{\int_{0}^{\frac{2\;\pi}{\;\omega}}{{p_{o}(t)}\ {\mathbb{d}t}}}} = {\frac{1}{2}V_{o}I_{o}}}}}}}} & (2)\end{matrix}$At

${t = {\pm \frac{\pi}{4\;\omega}}},$we have po(t)=P_(in), and if

$t \in \underset{\_}{\left( {{- \frac{\pi}{4\;\omega}},\frac{\pi}{4\;\omega}} \right),}$the input power will be greater than the output power. Therefore, forthis time period the inductor L_(A) will be charged from IL_(Amin) toIL_(Amax):

$\begin{matrix}{{{{\frac{1}{2}L_{A}{I_{L}^{2}}_{\;_{A}\max}} - {\frac{1}{2}L_{A}I_{L_{A}\min}^{2}}} = {{\int_{\frac{- \pi}{4\;\omega}}^{\frac{\pi}{4\;\omega}}{\left( {P_{in} - {p_{o}(t)}} \right)\ {\mathbb{d}t}}} = \left. \frac{P_{in}}{\omega}\Rightarrow \right.}}\;} & (3) \\{\;{{{\Delta\; I_{L}A} = \frac{P_{in}}{2\;\omega\; L_{A}{\overset{\_}{I}}_{L_{A}}}},{{\overset{\_}{I}}_{L_{A}} = \frac{I_{L_{A}\min} + I_{L_{A}\max}}{2}}}} & (4)\end{matrix}$

Since the inductor current is equal to its dc value at t=0, using asimilar procedure as described above the inductor current as a functionoft may be derived as follows:

$\begin{matrix}{{i_{L_{A}}(t)} = \sqrt{{\overset{\_}{I}}_{L_{A}}^{2} + {\frac{1}{2\;\omega\; L_{A}}V_{o}I_{o}\sin\; 2\;\omega\; t}}} & (5)\end{matrix}$

With reference to FIG. 6, control of the inductor dc component using themodulation index of the PWM may be explained as follows. By reducing themodulation index the output current is reduced temporarily.Consequently, the output power decreases and the difference energy isstored in the inductor which in turn increases its dc value. As aresult, the output current increases up to the point where the averagepower injected into the grid equals the input power.

To reduce the conduction losses and to obtain a flatter efficiencycurve, the inductor dc current may be minimized by the modulation indexfor different input power levels. Equations (4) and (5) show thatoscillation of the inductor current depends on the input power, theinductor value, and the inductor dc current. Thus, as the inductor dccurrent decreases, ΔI_(L) increases, which eventually results in adiscontinuous mode of operation where the output current becomesdistorted.

To avoid this mode of operation, the minimum of the inductor currentshould be higher than the maximum output current when the second stageis, for example, a voltage boost inverter or a step down current sourceinverter. If a voltage source inverter is utilized at the second stagethe oscillations will occur at the voltage of the inverter inputcapacitor. To avoid a discontinuous mode of operation the capacitorvoltage should be larger than the grid voltage, and a similar approachmay be used to derive equations for this mode of operation. Thus, thefollowing inequality has to be satisfied:

$\begin{matrix}{{{I_{L\;{dc}} - {\Delta\; I_{L}}} \geq I_{o}} = \left. \frac{2\; P_{in}}{V_{o}}\Rightarrow \right.} & (6) \\{\;{I_{L\;{dc}} \geq {\frac{P_{in}}{V_{o}} + \sqrt{\frac{P_{in}^{2}}{V_{o}^{2}} + \frac{P_{in}}{2\;\omega\; L}}}}} & (7)\end{matrix}$

The right hand side of the inequality forms the reference inductorcurrent. FIG. 7 shows an example of the case when the reference currentis too low and the grid current is distorted (see FIG. 9; low inductorcurrent reference). Since the minimum possible inductor current isdesired, the equality may be used in the controller system to generate areference signal for the inductor dc current, as shown in FIG. 7, timeinterval (t₁−t₂).

FIG. 7 shows a block diagram of an embodiment of the current sourceinverter control system, which consists of two parts: a proportionalintegral (PI) controller 100 to stabilize the inductor dc current leveland prevent discontinuous modes of operation; and a compensator 200 thatmodifies the PWM reference signal to cancel harmonics at the gridcurrent. To form the feedback loop, first the dc inductor value ismeasured and then the error signal is fed into the PI controller. Theoutput of the PI controller adjusts the amplitude of the output currentreference signal. When the error signal is positive, the inductor dccurrent is higher than the reference and has to be reduced. In this casethe PI controller increases the reference PWM signal and consequentlythe output current and power increase. This, in turn, decreases theinductor current until the error signal is zero where the output of thePI controller remains constant. The case where the error signal ispositive is similar. Since a PI controller is used, the steady stateerror will be zero and as a result, according to equation (7), theinductor current is always minimized to optimize conduction losses andalso to ensure that the output current will not become discontinuous.When there is more than one PV cell string connected to the circuit, theoutput power equals the sum of the input powers. Thus, the outputcurrent may be decomposed into components corresponding to each string,for example, i_(o)(t)=i_(o1)(t)+i_(o2)(t). However, the charging anddischarging of each inductor depends on the difference between the powergenerated by a string and the power injected to the system from thatstring. Therefore, equations (2), (4), and (5) hold true for any numberof PV cell strings j, if i_(o), p_(o), P_(in) and L_(A) are substitutedby i_(oj), p_(oj), P_(inj) and L_(X). If the inequality (6) is satisfiedfor each string for any condition, the sum of the inductors' currentswill be larger than the maximum output current. The reference currentfor each string is calculated and added together to form one referenceinductor current and as a result, the control strategy shown in FIG. 7regulates the dc inductor current of all strings. An embodiment for amulti string inverter is shown in FIG. 8.

A feature of this multi-string topology embodiment is that the outputpower oscillation is not supplied only by one inductor. Rather, allstrings contribute to the power oscillation. As a result, with morestrings, the current oscillation on each inductor is reduced and smallerinductors may be used. Moreover, because of the smaller oscillations,equation (5) results in a smaller dc reference for the inductorcurrents, which in turn reduces the conduction losses.

Harmonic Cancelation Method Using Modified PWM Technique

The embodiment described in the following section is based on a currentsource inverter (CSI). However, the method may be used to cancel anoscillation at the input of other converters, and in another embodimenta voltage source inverter (VSI) is used. The below description alsoapplies to a voltage source inverter, the only difference being that theinput source is voltage, the inductors are replaced by capacitors, andcurrents are replaced with voltages, and vice versa.

As shown in equation (5), the inductor current oscillates around a dcvalue at twice the grid frequency. Conventional sine PWM techniquesassume a constant dc input current, and thus any harmonic of the inputsource will be reflected to the modulated output current. This problemmay be avoided by introducing a compensation factor as shown in FIG. 7.When the oscillatory current source inverter input dc current increases,the compensator decreases the modulation index proportionally, which isdone by the multiplication of the signal labeled comp (t) and the sinePWM reference signal as shown in FIG. 7. As a result, an increase in thedc current value is compensated by a reduction in the modulation pulsewidth, and vice versa. This type of compensation prevents oscillatoryharmonics from appearing at the output current because the PWM modulatorcreates the new sine PWM reference signal at the output of the inverterand thus the energy transfer to the output is equivalent to the casewhere the inductor current is a constant dc current with no oscillation.The modulation signals and compensation method are shown in detail inFIG. 6. In FIG. 6(a) two cases when the inductor current is dc oroscillatory are demonstrated. FIG. 6(b) shows PWM reference and carriersignals for the above mentioned cases. As shown, the reference ismodified by a factor which shows how much the inductor current hasdeviated from the dc level. The effect of this modification is shown inFIGS. 6(b), (c) for the interval when the inductor current is higherthan the dc level. It can be observed from waveform (d) that since thecurrent is higher, the pulse width is lower than the dc current and bothwaveforms transfer the same amount of energy to the output. As a result,with this modification, the case where the inductor current isoscillatory, the harmonics at the output are similar to the case wherethe inductor current is pure dc. As explained above this modificationmay also be applied to the case where the second stage is a voltagesource inverter and the input voltage is oscillatory.

The following non-limiting example is provided to further illustrate theinvention.

Example

To demonstrate the impact of the irradiance level, input voltage level,and partial shading on the performance of a two-string PV cell inverteras shown in FIGS. 5B and 8, a simulation was carried out using PSIM 7.0software and the values set forth in Table I, and the results are shownin FIG. 10, The system was started with string #2 partially shaded (40%of the full irradiation level) and string #1 at full power. At t=0.2 (s)both strings were partially shaded at 15% of the full irradiation leveland the system response was obtained. At t=0.3 (s) the temperature ofthe PV cells was increased so that the output voltage of the PV cellsdecreased from 150V to 80V, which is less than the grid voltage. Att=0.4 (s) both strings were exposed to full irradiance. It can be seenfrom FIG. 10 that after each change, the controller quickly stabilizedthe output current. In addition, the maximum input power extraction wasalmost instantaneous, confirming the fast dynamic response of the MPPtracker circuit. Overall, the simulation results show that the converteris robust, and provides excellent decoupling performance formedium-power systems (such as residential applications).

TABLE I SIMULATION PARAMETERS Parameters Values C_(PV1), C_(PV2) 20 μFC_(f) 2 μF L_(A), L_(B) 2000 μH L_(f) 1000 μH CSI f_(s) 10 KHz Firststage f_(s) ^(max) 20 KHz Grid voltage 110 V Grid frequency 60 Hz PVString MPP 1.1 KW

The contents of all references, pending patent applications, andpublished patents cited throughout this application are hereby expresslyincorporated by reference.

Equivalents

Those skilled in the art will recognize or be able to ascertain variantsof the embodiments described herein. Such variants are within the scopeof the invention and are covered by the appended claims.

REFERENCES

-   [1] M. Meinhardt, G. Cramer, B. Burger, and P. Zacharias,    “Multi-string converter with reduced specific costs and enhanced    functionality,” Solar Energy, vol. 69, no. 1, pp. 217-27, 2000.-   [2] S. B. Kjaer, J. K. Pedersen, and F. Blaabjerg, “A review of    single-phase grid-connected inverters for photovoltaic modules,”    IEEE Transactions on industry Applications, vol. 41, no. 5, pp.    1292-1306, Sep./Oct. 2005.-   [3] G. Walker and P. Sernia, “Cascaded DC/DC converter connection of    photovoltaic modules,” IEEE Transactions on Power Electronics, vol.    19, pp. 1130-1139, 2004.-   [4] T. Esram and P. L. Chapman, “Comparison of photovoltaic array    maximum power point tracking techniques,” IEEE Transaction on Energy    Conversion, vol. 22, no. 2, pp. 439-449, Jun. 2007.-   [5] Y. Xue, L. Chang, S. B. Kjaer, J. Bordonau, and T. Shimizu,    “Topologies of single-phase inverters for small distributed power    generators: an overview,” IEEE Transactions on Power Electronics,    vol. 19, no. 5, pp. 1305-1314, Sep. 2004.-   [6] T. Shimizu, K. Wada, and N. Nakamura, “A flyback-type single    phase utility interactive inverter with low-frequency ripple current    reduction on the DC input for an AC photovoltaic module system,”    Power Electronics Specialists Conference, pesc 02. IEEE 33rd Annual,    vol. 3, pp. 1483-1488, 2002.-   [7] S. B. Kjaer and F. Blaabjerg, “Design optimization of a single    phase inverter for photovoltaic applications,” Power Electronics    Specialist Conference, PESC '03. IEEE 34th Annual, vol. 3, pp.    1183-1190, Jun. 2003.-   [8] B. M. T. Ho and H. S.-H. Chung, “An integrated inverter with    maximum power tracking for grid-connected PV systems,” IEEE    Transactions on Power Electronics, vol. 20, no. 4, pp. 953-962, Jul.    2005.

The invention claimed is:
 1. A compensator, comprising: an input thatreceives a signal corresponding to a voltage source inverter inputvoltage or a current source inverter input current and generates acompensation signal representing a deviation of the voltage sourceinverter input voltage or the current source inverter input current froma DC value; an input that receives a pulse width modulation referencesignal and modifies the pulse width modulation reference signalaccording to the compensation signal, and produce a modified pulse widthmodulation reference signal; and an output that provides the modifiedpulse width modulation reference signal to a pulse width modulator;wherein the modified pulse width modulation reference signal controlsthe pulse width modulator such that a harmonic in a voltage sourceinverter output current or a current source inverter output current issubstantially reduced; wherein the harmonic arises from voltage sourceinverter input voltage oscillation or current source inverter inputcurrent oscillation.
 2. The compensator of claim 1, wherein the pulsewidth modulation reference signal is modified in proportion to thecompensation signal; wherein the compensation signal is a ratio ofaverage and instantaneous values of the voltage source inverter inputvoltage or the current source inverter input current.
 3. The compensatorof claim 1, wherein: the voltage source inverter output current or thecurrent source inverter output current is connected to a powerdistribution grid having a grid frequency; and wherein at least oneharmonic that is substantially reduced is at a frequency that is twicethe grid frequency.
 4. The compensator of claim 1, wherein thecompensator is connected to a circuit comprising: a high side inputpoint and a low side input point for connection to a distributed powergenerator; a parallel input capacitor connected across the high sideinput point and the low side input point; and a first regulating circuitconnected in parallel with the parallel input capacitor, the firstregulating circuit having a high side output point connected to thevoltage source inverter input so as to provide the voltage sourceinverter input voltage; wherein the parallel input capacitor has a smallvalue such that voltage source inverter input voltage oscillation is notsubstantially reduced.
 5. The compensator of claim 4, wherein the firstregulating circuit comprises: a switch connected between the high sideinput point and a node; an output inductor connected between the nodeand the high side output point; and a diode connected between the nodeand a low side output point.
 6. The compensator of claim 4, wherein thefirst regulating circuit regulates voltage across the parallel inputcapacitor between a lower limit and an upper limit; wherein the upperlimit is a reference voltage and the lower limit is selected so that aswitching frequency of the switch and voltage oscillation across theparallel input capacitor do not exceed selected values.
 7. Thecompensator of claim 6, Wherein the reference voltage is obtained from amaximum power point tracking (MPPT) algorithm.
 8. The compensator ofclaim 1, wherein the compensator is connected to a circuit comprising: ahigh side input point and a low side input point for connection to adistributed power generator; a series input inductor having a firstterminal and a second terminal, the first terminal connected to one ofthe high side input point and the low side input point; and a secondregulating circuit connected between the second terminal of the seriesinput inductor and the other of the high side input point and the lowside input point, the second regulating circuit having a high sideoutput point connected to the current source inverter input so as toprovide the current source inverter input current; wherein the seriesinput inductor has a small value such that current source inverter inputcurrent oscillation is not substantially reduced.
 9. The compensator ofclaim 8, wherein the second regulating circuit comprises: a switchconnected between the second terminal of the series input inductor andthe other of the high side input point and the low side input point; anda diode connected in series between the second terminal of the seriesinput inductor and a corresponding high side output point or low sideoutput point.
 10. The compensator of claim 8, wherein the secondregulating circuit regulates current through the series input inductorbetween a lower limit and an upper limit; wherein the upper limit is areference current and the lower limit is selected so that a switchingfrequency of the switch and current oscillation through the series inputinductor do not exceed selected values.
 11. The compensator of claim 10,wherein the reference current is obtained from a maximum power pointtracking (MPPT) algorithm.
 12. The compensator of claim 4, wherein thedistributed power generator comprises a photovoltaic cell.
 13. Thecompensator of claim 8, Wherein the distributed power generatorcomprises a photovoltaic cell.
 14. A method for controlling a voltagesource inverter or a current source inverter, comprising: receiving asignal corresponding to an input voltage of the voltage source inverteror an input current of the current source inverter and generating acompensation signal representing a deviation of the voltage sourceinverter input voltage or the current source inverter input current froma DC value; modifying a pulse width modulation reference signalaccording to the compensation signal; and outputting the modified pulsewidth modulation reference signal to a pulse width modulator; whereinthe pulse width modulator controls a voltage source inverter or acurrent source inverter such that a harmonic in the voltage sourceinverter output current or current source inverter output current issubstantially reduced; wherein the harmonic arises from voltage sourceinverter input voltage oscillation or current source inverter inputcurrent oscillation.
 15. The method of claim 14, comprising modifyingthe pulse width modulation reference signal in proportion to thecompensation signal, wherein the compensation signal is a ratio ofaverage and instantaneous values of the voltage source inverter inputvoltage or the current source inverter input current.
 16. The method ofclaim 14, comprising: connecting the voltage source inverter outputcurrent or the current source inverter output current to a powerdistribution grid having a grid frequency; and substantially reducing atleast one harmonic at a frequency that is twice the grid frequency. 17.The method of claim 14, further comprising: using a first regulatingcircuit to provide the voltage source inverter input voltage, the firstregulating circuit including: a high side input point and a low sideinput point for connection to a distributed power generator; and aparallel input capacitor connected across the high side input point andthe low side input point; and selecting a small value of the parallelinput capacitor such that voltage source inverter input voltageoscillation is not substantially reduced.
 18. The method of claim 17,comprising: operating the first regulating circuit to regulate voltageacross the parallel input capacitor between a lower limit and an upperlimit; wherein the upper limit is a reference voltage; and selecting thelower limit so that a switching frequency of a switch of the firstregulating circuit and voltage oscillation across the parallel inputcapacitor do not exceed selected values.
 19. The method of claim 18,comprising obtaining the reference voltage from a maximum power pointtracking (MPPT) algorithm.
 20. The method of claim 14, furthercomprising: using a second regulating circuit to provide the currentsource inverter input current, the second regulating circuit including:a high side input point and a low side input point for connection to adistributed power generator; and a series input inductor connected inseries with the high side input point or the low side input point; andselecting a small value of the series input inductor such that currentsource inverter input current oscillation is not substantially reduced.21. The method of claim 20, comprising: operating the second regulatingcircuit to regulate current through the series input inductor between alower limit and an upper limit; wherein the upper limit is a referencecurrent; and selecting the lower limit so that a switching frequency ofa switch of the second regulating circuit and current oscillationthrough the series input inductor do not exceed selected values.
 22. Themethod of claim 21, comprising obtaining the reference current from amaximum power point tracking (MPPT) algorithm.
 23. The method of claim17, wherein the distributed power generator comprises a photovoltaiccell.
 24. The method of claim 20, wherein the distributed powergenerator comprises a photovoltaic cell.